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We derive loop equations for the one-link correlators of gauge and scalar fields in the Kazakov-Migdal model. These equations determine the solution of the model in the large N limit and are similar to analogous equations for the Hermitean two-matrix model. We give an explicit solution of the equations for the case of a Gaussian, quadratic potential. We also show how similar calculations in a non-Gaussian case reduce to purely algebraic equations.

We discuss the possibility for the spectrum of topologically massive quantum electrodynamics with spinor matter fields to contain unexpected and unusual stable particle excitations for certain values of the topological photon mass. The new field theoretical phenomena arising from this novel spectral structure are briefly discussed.

We review the present status of the problem of the six standard deviation discrepancy between the theoretical and experimental values of the orthopositronium lifetime. We discuss possible ways of its explanation and show that those invoking new decay modes are apparently closed. So the solution of this problem most probably lies either in large numerical value of the next, yet uncalculated, coefficient in the perturbative expansion of the orthopositronium decay width or in shortcomings of the standard treatment of the bound state problem in quantum field theory.

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